Browsing Mathematics Senior Individualized Projects by Title
Now showing items 227246 of 249

A Theorem on the Removal of Vertices from Blocks
(Kalamazoo College, 1968)As my Senior Independent Project, I studied graph theory. After my preliminary studies, amid several abortive attempts to investigate problems which I found appealing, I was confronted with a conjecture by Jerome J. ... 
Theory of Retracts
(Kalamazoo College, 1968)The paper is divided essentially into three parts. In the first, preliminary definitions are given, and the extension problem is defined. We see that from the extension problem, we encounter the retraction problem. The ... 
The Theory of TwoPerson Games
(Kalamazoo College, 1980)The term game theory suggests a theory applicable only to parlor games, poker, and the like. While the theory may be applied to parlor games, its actual scope is much wider. The theory may be applied to economic strategies, ... 
Tonnetz and Beyond : In Search of Functional Representations of Harmonic Structures through Algebra and Geometry
(Kalamazoo College, 2015)In this paper, we wish to explore underlying mathematical structures of tonal music with the use of group theoretic and geometric models. We will begin by examining trends in the current literature on the subject in attempts ... 
A Tool for Devising a Bridge Bidding System
(Kalamazoo College, 1968) 
Topological Groups
(Kalamazoo College, 1968)The purpose of this paper is to introduce the reader to the field of topological groups.  In the first two sections, we list definitions and theorems from topology and group theory which are used in proving the results ... 
Toward a Dialogical Model: Revisiting HumanMachine Interaction
(Kalamazoo College, 2002)In this paper, we suggest that we ought to develop humane interfaces to computation. We further suggest that this can be accomplished by constructing dialogical interfaces, that such interfaces provide models of interaction ... 
Transitional Trajectories Between Minimum Energy Conformations of Flexible Biomolecules
(Kalamazoo College, 2005)This paper describes conformational transitions of flexible biomolecules, especially proteins. Molecules tend to naturally occur in stable (or minimum energy) conformations. Dynamics methods can be used to model a molecule ... 
Translation of a Computer Program from Dynamo to CSMP10
(1972)My SIp started out to be simply to help the Center for Environmental Study (Grand Rapids, MI) staff with one of their ongoing projects, but after several talks with Mr. Nunn, it was decided that a translation from DYNAIvIO ... 
The True Permutations of the Bells
(Kalamazoo College, 2003)Change ringing is the art of ringing tower bells, dating back to the early 17th century. The "songs" (methods) rung are composed of permutations of the bells. Each permutation can occur only once in a method, or else the ... 
Twelfth Grade Mathematics: A Summary of Changes and a Review of New Possibilities
(Kalamazoo College, 1966)This paper evolved from my desire to learn more about new reforms in secondary school mathematics. Through conversations with Dr. Calloway, I decided that the twelfth grade offered the greatest number of possibilities. ... 
Understanding Rings of Invariant Polynomials
(Kalamazoo College, 2002)This paper is designed to introduce undergraduates with some knowledge of abstract algebra to the field of invariant theory. After defining representations and invariant polynomials, key theorems such as Noether's bound ... 
Unique Factorization Domains and Generalizations
(Kalamazoo College, 1987)The Fundamental Theorem of Arithmetic states that every integer greater than 1 is either a prime or the product of primes. This product is unique up to rearranging the order of the primes. Unique factorization is a ... 
The Unsolvability of a Fifth Degree Polynomial and Related Galois Theory
(Kalamazoo College, 1970)In retrospect, this paper has been divided into two related parts. First, after a preliminary example, we considered the fundamental theorem of Galois theory and related concepts, among them: a) extensions, b) normal ... 
Upjohn Job Report: GPSS Simulation of Credit and Collection Department
(Kalamazoo College, 1981)During the fall quarter, 1981, I served as an intern in the Management Science unit of the Information Management Services Division of The Upjohn Company in Portage, Michigan. Within the structure of The Upjohn Company, ... 
The Use of Automation in the Quality Assurance Endeavors of Software Development Companies
(Kalamazoo College, 2002)Quality assurance is a vast topic with many smaller divisions. It is used in virtually every industry in the world in some form or another. One interesting facet of the use of quality assurance is the use of automation ... 
User's Manuals for SimplexMethod Programs on the Western Michigan University Computer Program Library
(Kalamazoo College, 1981)The author created manuals for LINPRO and RVSLPR, two programs using the simplex method of solving linear programming problems. 
Using COBOL to Construct Commutation Columns
(Kalamazoo College, 1968)The purpose of this paper is to serve as an introduction to certain aspects of two fields: actuarial science and computer technology. More specifically, I have used the computer to prepare tables which are basic to ... 
Visualization of FourDimensional Objects
(20030120) 
Water Infiltration in Unsaturated Soils: A Comparison of Analytical and Numerical Solutions to Richards' Equation
(Kalamazoo College, 1994)We consider a mathematical model for a current problem in the fields of soil science and environmental engineering. We examine analytical and numerical solutions to Richards' equation, which describes the onedimensional ...